Proyecto Parcial 1: Regresión¶

Para este proyecto se utilizó una base de datos llamada Superconductivity Data obtenida del UCI Machine Learning Repository.

La base de diferentes datos y mediciones sobre 21263 materiales superconductores distintos. En total, en la base hay 81 variables de las cuales todas son de tipo numérico, algunos enteros y otros continuos.

La variable de interés es la Temperatura Crítica (critical_temp) ya que esta es una característica muy importante en la aplicación de superconductores en la ingeniería, y poder predecir cual sera la temperatura crítica de un superconductor puede contribuir a la integración de superconductores en nuevas tecnologías.

In [11]:
import pandas as pd
df = pd.read_csv("train.csv")
print("Número de Observaciones:",df.shape[0])
print("Número de Variables:",df.shape[1]-1)
print("Variable de interes:",df.columns.tolist()[81])
print("\nTodas las Variables:")
for i in df.columns:
  print("-",i)
Número de Observaciones: 21263
Número de Variables: 81
Variable de interes: critical_temp

Todas las Variables:
- number_of_elements
- mean_atomic_mass
- wtd_mean_atomic_mass
- gmean_atomic_mass
- wtd_gmean_atomic_mass
- entropy_atomic_mass
- wtd_entropy_atomic_mass
- range_atomic_mass
- wtd_range_atomic_mass
- std_atomic_mass
- wtd_std_atomic_mass
- mean_fie
- wtd_mean_fie
- gmean_fie
- wtd_gmean_fie
- entropy_fie
- wtd_entropy_fie
- range_fie
- wtd_range_fie
- std_fie
- wtd_std_fie
- mean_atomic_radius
- wtd_mean_atomic_radius
- gmean_atomic_radius
- wtd_gmean_atomic_radius
- entropy_atomic_radius
- wtd_entropy_atomic_radius
- range_atomic_radius
- wtd_range_atomic_radius
- std_atomic_radius
- wtd_std_atomic_radius
- mean_Density
- wtd_mean_Density
- gmean_Density
- wtd_gmean_Density
- entropy_Density
- wtd_entropy_Density
- range_Density
- wtd_range_Density
- std_Density
- wtd_std_Density
- mean_ElectronAffinity
- wtd_mean_ElectronAffinity
- gmean_ElectronAffinity
- wtd_gmean_ElectronAffinity
- entropy_ElectronAffinity
- wtd_entropy_ElectronAffinity
- range_ElectronAffinity
- wtd_range_ElectronAffinity
- std_ElectronAffinity
- wtd_std_ElectronAffinity
- mean_FusionHeat
- wtd_mean_FusionHeat
- gmean_FusionHeat
- wtd_gmean_FusionHeat
- entropy_FusionHeat
- wtd_entropy_FusionHeat
- range_FusionHeat
- wtd_range_FusionHeat
- std_FusionHeat
- wtd_std_FusionHeat
- mean_ThermalConductivity
- wtd_mean_ThermalConductivity
- gmean_ThermalConductivity
- wtd_gmean_ThermalConductivity
- entropy_ThermalConductivity
- wtd_entropy_ThermalConductivity
- range_ThermalConductivity
- wtd_range_ThermalConductivity
- std_ThermalConductivity
- wtd_std_ThermalConductivity
- mean_Valence
- wtd_mean_Valence
- gmean_Valence
- wtd_gmean_Valence
- entropy_Valence
- wtd_entropy_Valence
- range_Valence
- wtd_range_Valence
- std_Valence
- wtd_std_Valence
- critical_temp

Huecos¶

La base de datos cuenta con algunos huecos los cuales fueron detectados al momento de intentar generar un modelo de regresión lineal con los datos sin procesar, a manera de prueba. Para resolver esto, se utiliza la funcion dropna() de pandas y se elimina toda aquella columna con huecos NaN.

In [25]:
df = df.dropna()
15667

Outliers¶

Para identificar valores atípicos, se utiliza el método de Tukey y se calcula el rango intercuartíl de todas y cada una de las variables y se eliminan las columnas que tengan valores fuera del rango. Tras esta acción, se reduce el número de observaciones.

In [13]:
import numpy as np
df_filtrado = df.copy()
for column in df.columns:
  Q1 = df[column].quantile(0.25)
  Q3 = df[column].quantile(0.75)
  IQR = Q3-Q1
  lower_bound = Q1 - 3 * IQR
  upper_bound = Q3 + 3 * IQR
  df_filtrado = df_filtrado[(df_filtrado[column] >= lower_bound) & (df_filtrado[column] <= upper_bound)]
print("Nuevo número de observaciones:",df_filtrado.shape[0])
df= df_filtrado
Nuevo número de observaciones: 15667

Colinearidad¶

En esta base de datos, muchas de las variables son medias u otros estadísticos de una misma variable, por lo cual pueden provocar colinearidad. Para identificar si existe este problema se genera un heatmap donde se muestre visualmente, una matriz de correlaciones entre las variables.

In [14]:
import seaborn as sns
import matplotlib.pyplot as plt
y = df['critical_temp']
x = df.drop(columns = ['critical_temp'])
corr_matrix = x.corr()
plt.figure(figsize=(100,100))
sns.heatmap(corr_matrix, annot=True, cmap="coolwarm",fmt=".2f",linewidths=0.5)
plt.title("Correlation Matrix Heatmap")
plt.show()
No description has been provided for this image

Como era esperado, hay una gran cantidad de variables que muestran colinealidad alta, para erradicar esto, de cada par de variables con correlación mayor o igual a 0.9, se eliminará una de ellas. Tras esto se reduce el número de variables.

In [15]:
column_purge = set()
for i in range(len(corr_matrix.columns)):
  for j in range(i + 1, len(corr_matrix.columns)):
    if abs(corr_matrix.iloc[i, j]) >= 0.9:
      colname = corr_matrix.columns[j]
      column_purge.add(colname)
x = x.drop(columns = column_purge)
print(f"columnas eliminadas por alta correlación: {column_purge}")

corr_matrix = x.corr()
plt.figure(figsize=(25,25))
sns.heatmap(corr_matrix, annot=True, cmap="coolwarm",fmt=".2f",linewidths=0.5)
plt.title("Correlation Matrix Heatmap")
plt.show()
print("Nuevo número de variables:",x.shape[1])
columnas eliminadas por alta correlación: {'wtd_std_ElectronAffinity', 'wtd_entropy_Valence', 'wtd_std_atomic_radius', 'std_Density', 'wtd_gmean_Density', 'wtd_gmean_atomic_mass', 'gmean_fie', 'std_atomic_radius', 'entropy_atomic_mass', 'gmean_Density', 'std_ThermalConductivity', 'wtd_entropy_atomic_radius', 'wtd_gmean_fie', 'wtd_std_Density', 'entropy_Valence', 'wtd_std_ThermalConductivity', 'wtd_mean_atomic_radius', 'wtd_std_atomic_mass', 'std_fie', 'gmean_FusionHeat', 'gmean_Valence', 'entropy_Density', 'range_atomic_radius', 'entropy_FusionHeat', 'wtd_gmean_FusionHeat', 'wtd_std_fie', 'wtd_std_FusionHeat', 'std_Valence', 'std_atomic_mass', 'wtd_gmean_Valence', 'wtd_range_ThermalConductivity', 'entropy_atomic_radius', 'wtd_mean_Valence', 'std_FusionHeat', 'wtd_gmean_atomic_radius', 'entropy_fie', 'std_ElectronAffinity', 'wtd_mean_FusionHeat'}
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Nuevo número de variables: 43

División de Datos¶

Para comenzar a entrenar modelos se debe dividir la base de datos en 2. Para esto se usa la función train_test_split ya que el siguiente paso el realizar una selección de características donde se requiere generar varios modelos de regresión.

In [16]:
from sklearn.model_selection import train_test_split
x_train, x_test, y_train, y_test = train_test_split(x,y,test_size = 0.3, random_state = 23)

Selección de Características¶

Para seleccionar las características que serán utilizadas en los modelos de regresión, se utilizará un modelo de selección hacia adelante.

In [17]:
from sklearn.linear_model import LinearRegression
from mlxtend.feature_selection import SequentialFeatureSelector as SFS
from sklearn.metrics import r2_score
model = LinearRegression()
model.fit(x_train, y_train)
sfs_f = SFS(model, k_features = 'best', forward = True, scoring = 'r2', cv = 10, verbose = 1)
sfs_f.fit(x_train, y_train)
selected_features_f = list(sfs_f.k_feature_names_)
print("\n✅ Características seleccionadas:")
print(f"Índices: {sfs_f.k_feature_idx_}")
print(f"Nombres: {selected_features_f}")

x_selected_train = x_train[selected_features_f]
x_selected_test = x_test[selected_features_f]
Features: 43/43
✅ Características seleccionadas:
Índices: (0, 1, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42)
Nombres: ['number_of_elements', 'mean_atomic_mass', 'gmean_atomic_mass', 'wtd_entropy_atomic_mass', 'range_atomic_mass', 'wtd_range_atomic_mass', 'mean_fie', 'wtd_mean_fie', 'wtd_entropy_fie', 'mean_atomic_radius', 'gmean_atomic_radius', 'wtd_range_atomic_radius', 'mean_Density', 'wtd_entropy_Density', 'range_Density', 'wtd_range_Density', 'mean_ElectronAffinity', 'wtd_mean_ElectronAffinity', 'wtd_gmean_ElectronAffinity', 'entropy_ElectronAffinity', 'wtd_entropy_ElectronAffinity', 'range_ElectronAffinity', 'wtd_range_ElectronAffinity', 'mean_FusionHeat', 'wtd_entropy_FusionHeat', 'range_FusionHeat', 'wtd_range_FusionHeat', 'mean_ThermalConductivity', 'wtd_mean_ThermalConductivity', 'gmean_ThermalConductivity', 'wtd_gmean_ThermalConductivity', 'entropy_ThermalConductivity', 'wtd_entropy_ThermalConductivity', 'range_ThermalConductivity', 'mean_Valence', 'range_Valence', 'wtd_range_Valence', 'wtd_std_Valence']

Se utilizó el método de selección hacia adelante debido a que se busca un modelo con el menor número de variables posibles para que tenga un mejor rendimiento. El número de variables disminuyó, lo cual hará el entrenamiento del modelo más fácil de llevar a nivel computacional y también lo hace más interpretable.

Modelo de Regresión Lineal¶

Primero se genera un modelo de regresión lineal utilizando la función LinearRegression de sklearn.linear_model.

Modifiqué las variables de entrada para que solo tomaran en cuenta las variables seleccionadas tras el proceso de selección de características. Utilizando la función fit() se entreno el modelo con los datos de entrenamiento y después con la función predict() se probó el modelo con los datos de prueba. También se uso la función r2_score y se calculo la R^2 del modelo para conocer su desempeño. La gráfica muestra el desempeño del modelo contra los valores reales.

In [18]:
model.fit(x_selected_train, y_train)

y_pred = model.predict(x_selected_test)

r2_linear = r2_score(y_test,y_pred)
plt.scatter(y_test, y_pred)
plt.xlabel("Temperatura Crítica Real")
plt.ylabel("Temperatura Crítica Estimada")
print(f"\n📊 R^2 en datos de prueba: {r2_linear:.4f}")
📊 R^2 en datos de prueba: 0.6561
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Modelo de Regresión Polinomial¶

Ahora se probará un modelo de regresión polinomial. Para este se usa la función PolynomialFeatures de sklearn.preprocessing. Se usa un grado de 2 para equilibrar entre eficiencia computacional y buena calidad. Se transforman los datos con la función fit_transform y de nuevo utilizando la función LinearRegression se entrena el modelo polinomial. Una vez entrenado, se prueba con los datos de validación y se calcula su R^2. La gráfica muestra el desempeño del modelo contra los valores reales.

In [42]:
from sklearn.preprocessing import PolynomialFeatures

poly = PolynomialFeatures(degree=2)
x_poly_train = poly.fit_transform(x_selected_train)
x_poly_test = poly.fit_transform(x_selected_test)
model = LinearRegression()
model.fit(x_poly_train, y_train)


yhat_poly = model.predict(x_poly_test)

r2_poly = r2_score(y_test,yhat_poly)
print("R^2:",r2_poly)
plt.scatter(y_test,yhat_poly, color = "red",alpha = 0.5, label="Regresión Polinomial")
plt.title("Regresión Polinomial")
plt.xlabel("Temperatura Crítica Real")
plt.ylabel("Temperatura Crítica Estimada")
plt.legend()
plt.grid(True)
plt.show()
R^2: 0.7827518846207967
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Métricas de Error y Linealidad¶

Para comparar ambos modelos se calcula el mean square error (MSE) y la R^2 de ambos modelos de acuerdo con el desempeño de sus predicciones en los datos de validación.

In [43]:
from sklearn.metrics import mean_squared_error

mse_poly = mean_squared_error(y_test,yhat_poly)
mse_linear = mean_squared_error(y_test,y_pred)
print("MSE de Regresión Lineal:",mse_linear)
print("R^2 de Regresión Lineal:",r2_linear)
print("MSE de Regresión Polinomial:",mse_poly)
print("R^2 de Regresión Polinomial:",r2_poly)
MSE de Regresión Lineal: 407.421780417495
R^2 de Regresión Lineal: 0.656058819903386
MSE de Regresión Polinomial: 257.3452063381222
R^2 de Regresión Polinomial: 0.7827518846207967

Tras comparar ambos modelos, el modelo de regresión polinomial es el claro ganador ya que tiene un menor error (MSE) y un mayor nivel de linealidad (R^2) por lo tanto será el modelo seleccionado.

Inferencia con el Modelo¶

Tras obtener el modelo ganador, se utiliza la librería statsmodels.api para obtener información relevante para generar inferencias a partir del modelo.

In [44]:
import statsmodels.api as sm
poly_inf = sm.OLS(y_train,x_poly_train).fit()
print(poly_inf.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:          critical_temp   R-squared:                       0.831
Model:                            OLS   Adj. R-squared:                  0.818
Method:                 Least Squares   F-statistic:                     64.09
Date:                Thu, 20 Feb 2025   Prob (F-statistic):               0.00
Time:                        06:36:51   Log-Likelihood:                -44811.
No. Observations:               10966   AIC:                         9.118e+04
Df Residuals:                   10186   BIC:                         9.688e+04
Df Model:                         779                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const       -516.0799    370.659     -1.392      0.164   -1242.645     210.485
x1           -10.9082     68.357     -0.160      0.873    -144.901     123.084
x2             8.7944      4.549      1.933      0.053      -0.123      17.712
x3           -10.7145      4.370     -2.452      0.014     -19.280      -2.149
x4           529.8335    278.452      1.903      0.057     -15.987    1075.654
x5            -2.6347      0.909     -2.897      0.004      -4.417      -0.852
x6             3.6937      1.848      1.998      0.046       0.070       7.317
x7             1.0021      0.762      1.316      0.188      -0.491       2.495
x8            -0.0353      0.617     -0.057      0.954      -1.244       1.174
x9          -218.0254    270.618     -0.806      0.420    -748.489     312.438
x10            1.3011      6.036      0.216      0.829     -10.531      13.133
x11            1.4149      6.892      0.205      0.837     -12.094      14.924
x12            1.6817      1.036      1.623      0.105      -0.350       3.713
x13           -0.0010      0.025     -0.040      0.968      -0.050       0.048
x14          603.6378    269.446      2.240      0.025      75.470    1131.805
x15            0.0003      0.010      0.034      0.973      -0.020       0.020
x16            0.0116      0.024      0.479      0.632      -0.036       0.059
x17            1.1129      2.385      0.467      0.641      -3.563       5.789
x18            4.8201      4.902      0.983      0.325      -4.789      14.429
x19           -0.9670      3.674     -0.263      0.792      -8.169       6.235
x20         -106.9873    203.615     -0.525      0.599    -506.112     292.137
x21         -394.9268    233.534     -1.691      0.091    -852.699      62.845
x22           -1.0258      1.038     -0.988      0.323      -3.061       1.010
x23           -3.4095      2.430     -1.403      0.161      -8.173       1.354
x24            5.2595      6.556      0.802      0.422      -7.591      18.110
x25         -506.4936    201.017     -2.520      0.012    -900.527    -112.461
x26            0.8163      2.867      0.285      0.776      -4.803       6.435
x27           -7.1118      6.839     -1.040      0.298     -20.518       6.295
x28            0.9293      2.284      0.407      0.684      -3.548       5.407
x29            4.7342      1.598      2.963      0.003       1.602       7.866
x30           -1.7906      2.362     -0.758      0.448      -6.420       2.839
x31           -3.4320      2.064     -1.663      0.096      -7.478       0.614
x32         -205.2880    181.079     -1.134      0.257    -560.239     149.663
x33          226.7734    136.363      1.663      0.096     -40.525     494.072
x34           -0.5566      0.761     -0.731      0.465      -2.049       0.935
x35          -52.0638     45.572     -1.142      0.253    -141.394      37.267
x36            9.4912     35.094      0.270      0.787     -59.299      78.282
x37          -50.3646     37.573     -1.340      0.180    -124.015      23.286
x38           43.8329     91.948      0.477      0.634    -136.403     224.069
x39           -5.7850      3.710     -1.559      0.119     -13.057       1.486
x40            0.7475      0.395      1.892      0.059      -0.027       1.522
x41           -0.4907      0.410     -1.198      0.231      -1.294       0.313
x42            4.5227     26.066      0.174      0.862     -46.573      55.618
x43           -0.1069      0.078     -1.377      0.168      -0.259       0.045
x44           -0.2229      0.237     -0.942      0.346      -0.687       0.241
x45            0.1295      0.067      1.936      0.053      -0.002       0.261
x46           -0.0643      0.061     -1.061      0.288      -0.183       0.054
x47          -64.0233     23.791     -2.691      0.007    -110.657     -17.389
x48           -2.2702      0.595     -3.816      0.000      -3.436      -1.104
x49            2.3054      0.688      3.352      0.001       0.957       3.653
x50            0.1022      0.123      0.833      0.405      -0.138       0.343
x51           -0.0052      0.003     -1.809      0.071      -0.011       0.000
x52            6.5109     24.746      0.263      0.792     -41.996      55.017
x53           -0.0006      0.001     -0.586      0.558      -0.002       0.001
x54            0.0060      0.003      1.894      0.058      -0.000       0.012
x55           -0.1460      0.242     -0.602      0.547      -0.621       0.329
x56            0.4647      0.441      1.054      0.292      -0.399       1.329
x57           -0.5527      0.311     -1.777      0.076      -1.162       0.057
x58           39.8594     21.383      1.864      0.062      -2.056      81.774
x59           60.1410     24.791      2.426      0.015      11.545     108.737
x60            0.1254      0.098      1.285      0.199      -0.066       0.317
x61            0.1307      0.300      0.436      0.663      -0.457       0.718
x62           -0.6929      0.881     -0.786      0.432      -2.421       1.035
x63           -9.3110     19.808     -0.470      0.638     -48.139      29.517
x64            0.7284      0.243      2.995      0.003       0.252       1.205
x65           -0.4463      0.912     -0.489      0.625      -2.234       1.341
x66            0.0820      0.210      0.390      0.697      -0.330       0.494
x67            0.2060      0.145      1.423      0.155      -0.078       0.490
x68           -0.2679      0.254     -1.054      0.292      -0.766       0.230
x69           -0.2632      0.207     -1.268      0.205      -0.670       0.144
x70            3.6663     18.705      0.196      0.845     -32.999      40.331
x71           21.7815     11.647      1.870      0.061      -1.049      44.612
x72            0.0752      0.075      1.002      0.317      -0.072       0.222
x73          -15.4993      5.060     -3.063      0.002     -25.417      -5.582
x74           -2.3348      2.725     -0.857      0.392      -7.676       3.007
x75            7.3668      4.812      1.531      0.126      -2.067      16.800
x76            0.2018      7.571      0.027      0.979     -14.638      15.041
x77            0.0337      0.019      1.760      0.078      -0.004       0.071
x78           -0.0659      0.034     -1.944      0.052      -0.132       0.001
x79            0.9365      1.792      0.522      0.601      -2.577       4.450
x80            0.0134      0.007      1.788      0.074      -0.001       0.028
x81           -0.0725      0.017     -4.332      0.000      -0.105      -0.040
x82            0.0090      0.004      2.017      0.044       0.000       0.018
x83           -0.0149      0.004     -4.131      0.000      -0.022      -0.008
x84           -8.3554      1.682     -4.969      0.000     -11.651      -5.059
x85           -0.1013      0.037     -2.770      0.006      -0.173      -0.030
x86            0.1018      0.042      2.433      0.015       0.020       0.184
x87           -0.0031      0.008     -0.391      0.696      -0.018       0.012
x88           -0.0004      0.000     -1.539      0.124      -0.001    9.88e-05
x89           -0.1823      1.815     -0.100      0.920      -3.740       3.375
x90           -0.0002   8.48e-05     -1.914      0.056      -0.000    3.88e-06
x91            0.0012      0.000      5.985      0.000       0.001       0.002
x92            0.0085      0.016      0.518      0.605      -0.024       0.041
x93            0.1065      0.030      3.506      0.000       0.047       0.166
x94           -0.0825      0.023     -3.641      0.000      -0.127      -0.038
x95            1.8145      1.420      1.278      0.201      -0.968       4.597
x96            1.9861      1.729      1.149      0.251      -1.403       5.375
x97           -0.0042      0.007     -0.631      0.528      -0.017       0.009
x98           -0.0342      0.018     -1.904      0.057      -0.069       0.001
x99            0.0094      0.058      0.161      0.872      -0.105       0.123
x100          -0.1742      1.347     -0.129      0.897      -2.815       2.467
x101          -0.0446      0.020     -2.242      0.025      -0.084      -0.006
x102          -0.0156      0.060     -0.257      0.797      -0.134       0.103
x103           0.0313      0.016      1.976      0.048       0.000       0.062
x104          -0.0052      0.009     -0.568      0.570      -0.023       0.013
x105          -0.0190      0.018     -1.080      0.280      -0.053       0.015
x106          -0.0091      0.014     -0.647      0.518      -0.037       0.019
x107           0.1508      1.233      0.122      0.903      -2.265       2.567
x108           0.8221      0.840      0.979      0.328      -0.824       2.468
x109          -0.0075      0.005     -1.435      0.151      -0.018       0.003
x110          -0.2029      0.350     -0.580      0.562      -0.888       0.482
x111           0.2133      0.191      1.116      0.265      -0.161       0.588
x112          -0.6984      0.322     -2.171      0.030      -1.329      -0.068
x113          -1.1536      0.533     -2.166      0.030      -2.198      -0.110
x114           0.0190      0.017      1.120      0.263      -0.014       0.052
x115           1.0663      1.839      0.580      0.562      -2.538       4.670
x116          -0.0076      0.007     -1.088      0.277      -0.021       0.006
x117           0.0706      0.017      4.267      0.000       0.038       0.103
x118          -0.0054      0.004     -1.256      0.209      -0.014       0.003
x119           0.0112      0.003      3.194      0.001       0.004       0.018
x120           7.7507      1.690      4.586      0.000       4.438      11.063
x121           0.0823      0.036      2.280      0.023       0.012       0.153
x122          -0.0627      0.041     -1.526      0.127      -0.143       0.018
x123          -0.0060      0.008     -0.740      0.459      -0.022       0.010
x124           0.0007      0.000      2.885      0.004       0.000       0.001
x125          -2.9379      1.846     -1.592      0.111      -6.556       0.680
x126        7.221e-05   8.04e-05      0.898      0.369   -8.54e-05       0.000
x127          -0.0012      0.000     -6.104      0.000      -0.002      -0.001
x128           0.0056      0.017      0.340      0.734      -0.027       0.038
x129          -0.1110      0.032     -3.454      0.001      -0.174      -0.048
x130           0.0846      0.024      3.515      0.000       0.037       0.132
x131          -2.0461      1.491     -1.372      0.170      -4.969       0.876
x132          -1.7892      1.771     -1.011      0.312      -5.260       1.681
x133           0.0019      0.007      0.280      0.779      -0.011       0.015
x134           0.0328      0.018      1.820      0.069      -0.003       0.068
x135          -0.0791      0.054     -1.465      0.143      -0.185       0.027
x136           1.0860      1.388      0.783      0.434      -1.634       3.806
x137           0.0445      0.019      2.340      0.019       0.007       0.082
x138           0.0460      0.057      0.802      0.423      -0.066       0.158
x139          -0.0538      0.017     -3.224      0.001      -0.087      -0.021
x140           0.0073      0.010      0.754      0.451      -0.012       0.026
x141           0.0413      0.017      2.366      0.018       0.007       0.076
x142       -9.359e-05      0.014     -0.007      0.995      -0.028       0.028
x143          -0.4270      1.248     -0.342      0.732      -2.874       2.020
x144          -0.1438      0.858     -0.168      0.867      -1.825       1.537
x145           0.0130      0.005      2.389      0.017       0.002       0.024
x146           0.0955      0.337      0.283      0.777      -0.566       0.757
x147          -0.1677      0.203     -0.827      0.408      -0.565       0.230
x148           0.7975      0.319      2.498      0.012       0.172       1.423
x149           1.2073      0.558      2.165      0.030       0.114       2.300
x150         106.1840     86.318      1.230      0.219     -63.016     275.384
x151          -1.0685      0.360     -2.965      0.003      -1.775      -0.362
x152           2.9314      1.239      2.367      0.018       0.504       5.359
x153          -0.5616      0.289     -1.946      0.052      -1.127       0.004
x154           0.1441      0.261      0.552      0.581      -0.368       0.656
x155         369.1466    120.059      3.075      0.002     133.807     604.486
x156          -0.3439      2.504     -0.137      0.891      -5.251       4.564
x157          -2.2098      2.920     -0.757      0.449      -7.934       3.515
x158          -0.3143      0.544     -0.578      0.563      -1.380       0.752
x159           0.0025      0.012      0.199      0.842      -0.022       0.027
x160        -194.4540    127.062     -1.530      0.126    -443.520      54.612
x161           0.0129      0.004      2.890      0.004       0.004       0.022
x162          -0.0571      0.013     -4.372      0.000      -0.083      -0.031
x163          -0.5189      1.004     -0.517      0.605      -2.487       1.449
x164          -2.2037      1.958     -1.126      0.260      -6.042       1.634
x165           1.8599      1.416      1.313      0.189      -0.916       4.636
x166        -176.7681     88.810     -1.990      0.047    -350.853      -2.683
x167          18.3103    108.796      0.168      0.866    -194.952     231.572
x168          -0.2754      0.421     -0.654      0.513      -1.101       0.550
x169           1.1307      1.177      0.961      0.337      -1.176       3.437
x170          10.4962      3.387      3.099      0.002       3.856      17.136
x171         -48.8451     86.890     -0.562      0.574    -219.167     121.477
x172          -3.1852      1.111     -2.868      0.004      -5.362      -1.008
x173           2.3511      3.377      0.696      0.486      -4.268       8.970
x174           2.0975      0.913      2.297      0.022       0.308       3.887
x175          -2.0227      0.677     -2.986      0.003      -3.351      -0.695
x176          -3.5517      1.024     -3.469      0.001      -5.559      -1.545
x177           2.6036      0.984      2.646      0.008       0.675       4.532
x178          43.9963     74.313      0.592      0.554    -101.671     189.664
x179        -149.8787     55.464     -2.702      0.007    -258.598     -41.159
x180          -0.0409      0.312     -0.131      0.896      -0.652       0.571
x181         -13.5899     20.047     -0.678      0.498     -52.887      25.707
x182          -9.7702     12.291     -0.795      0.427     -33.864      14.323
x183          31.5920     20.716      1.525      0.127      -9.016      72.200
x184           7.5337     35.930      0.210      0.834     -62.896      77.963
x185          -0.0036      0.001     -4.015      0.000      -0.005      -0.002
x186           0.0098      0.003      3.250      0.001       0.004       0.016
x187          -0.0006      0.001     -0.685      0.494      -0.002       0.001
x188           0.0024      0.001      3.086      0.002       0.001       0.004
x189           0.5402      0.338      1.596      0.110      -0.123       1.204
x190           0.0415      0.008      5.246      0.000       0.026       0.057
x191          -0.0389      0.009     -4.223      0.000      -0.057      -0.021
x192          -0.0027      0.002     -1.733      0.083      -0.006       0.000
x193         2.71e-05    4.3e-05      0.630      0.529   -5.73e-05       0.000
x194           0.1744      0.359      0.486      0.627      -0.529       0.877
x195         2.33e-05   1.59e-05      1.461      0.144   -7.96e-06    5.46e-05
x196          -0.0002   3.71e-05     -5.770      0.000      -0.000      -0.000
x197          -0.0057      0.003     -1.763      0.078      -0.012       0.001
x198          -0.0062      0.006     -1.034      0.301      -0.018       0.006
x199           0.0047      0.004      1.071      0.284      -0.004       0.013
x200          -0.5655      0.283     -1.999      0.046      -1.120      -0.011
x201           0.6618      0.327      2.022      0.043       0.020       1.304
x202          -0.0004      0.001     -0.298      0.766      -0.003       0.002
x203           0.0038      0.003      1.113      0.266      -0.003       0.010
x204          -0.0224      0.011     -2.022      0.043      -0.044      -0.001
x205           0.2506      0.261      0.961      0.336      -0.260       0.762
x206           0.0074      0.004      1.993      0.046       0.000       0.015
x207           0.0219      0.011      1.911      0.056      -0.001       0.044
x208          -0.0107      0.003     -3.459      0.001      -0.017      -0.005
x209           0.0025      0.002      1.385      0.166      -0.001       0.006
x210           0.0057      0.003      1.766      0.077      -0.001       0.012
x211           0.0007      0.003      0.273      0.785      -0.005       0.006
x212           0.6943      0.245      2.829      0.005       0.213       1.175
x213          -0.1131      0.159     -0.711      0.477      -0.425       0.199
x214           0.0037      0.001      3.597      0.000       0.002       0.006
x215           0.1684      0.068      2.473      0.013       0.035       0.302
x216          -0.0722      0.035     -2.094      0.036      -0.140      -0.005
x217           0.2024      0.061      3.307      0.001       0.082       0.322
x218           0.2958      0.105      2.825      0.005       0.091       0.501
x219           0.0014      0.005      0.292      0.771      -0.008       0.011
x220          -0.0025      0.002     -1.064      0.287      -0.007       0.002
x221           0.0012      0.002      0.579      0.563      -0.003       0.005
x222           1.9921      1.025      1.944      0.052      -0.017       4.001
x223          -0.0058      0.020     -0.291      0.771      -0.045       0.033
x224          -0.0150      0.022     -0.674      0.500      -0.059       0.029
x225           0.0084      0.004      2.270      0.023       0.001       0.016
x226        5.708e-05   7.56e-05      0.755      0.450   -9.11e-05       0.000
x227          -2.3758      1.023     -2.323      0.020      -4.381      -0.371
x228        4.112e-05   2.88e-05      1.426      0.154   -1.54e-05    9.77e-05
x229          -0.0001   8.16e-05     -1.484      0.138      -0.000    3.89e-05
x230          -0.0035      0.008     -0.451      0.652      -0.019       0.012
x231          -0.0008      0.016     -0.053      0.957      -0.032       0.030
x232           0.0121      0.012      1.036      0.300      -0.011       0.035
x233           0.2641      0.736      0.359      0.720      -1.179       1.707
x234          -2.7652      0.864     -3.202      0.001      -4.458      -1.072
x235          -0.0034      0.003     -1.023      0.306      -0.010       0.003
x236          -0.0052      0.008     -0.675      0.500      -0.020       0.010
x237           0.0444      0.020      2.216      0.027       0.005       0.084
x238           0.5625      0.716      0.786      0.432      -0.840       1.965
x239          -0.0135      0.008     -1.637      0.102      -0.030       0.003
x240           0.0106      0.025      0.423      0.672      -0.039       0.060
x241           0.0039      0.008      0.458      0.647      -0.013       0.021
x242           0.0070      0.006      1.186      0.236      -0.005       0.019
x243          -0.0097      0.009     -1.038      0.299      -0.028       0.009
x244          -0.0054      0.008     -0.649      0.517      -0.022       0.011
x245          -0.5167      0.597     -0.865      0.387      -1.688       0.654
x246           0.4208      0.508      0.828      0.408      -0.575       1.417
x247          -0.0029      0.003     -1.092      0.275      -0.008       0.002
x248          -0.0743      0.127     -0.585      0.559      -0.323       0.175
x249           0.2586      0.119      2.179      0.029       0.026       0.491
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x251          -0.6881      0.299     -2.305      0.021      -1.273      -0.103
x252          -0.0013      0.001     -2.163      0.031      -0.002      -0.000
x253           0.0013      0.001      1.653      0.098      -0.000       0.003
x254           0.2897      0.300      0.965      0.335      -0.299       0.878
x255          -0.0020      0.006     -0.336      0.737      -0.014       0.010
x256          -0.0018      0.007     -0.262      0.793      -0.016       0.012
x257          -0.0017      0.001     -1.229      0.219      -0.004       0.001
x258        3.087e-05   2.94e-05      1.051      0.293   -2.67e-05    8.85e-05
x259           0.0902      0.269      0.336      0.737      -0.437       0.617
x260        1.146e-05   1.08e-05      1.063      0.288   -9.67e-06    3.26e-05
x261       -2.435e-05   3.11e-05     -0.783      0.434   -8.53e-05    3.66e-05
x262           0.0045      0.003      1.571      0.116      -0.001       0.010
x263          -0.0095      0.005     -1.885      0.060      -0.019       0.000
x264          -0.0003      0.004     -0.085      0.932      -0.007       0.007
x265          -0.1493      0.218     -0.684      0.494      -0.577       0.278
x266           0.5133      0.265      1.935      0.053      -0.007       1.033
x267          -0.0008      0.001     -0.875      0.382      -0.003       0.001
x268           0.0054      0.003      1.698      0.090      -0.001       0.012
x269          -0.0075      0.009     -0.795      0.426      -0.026       0.011
x270          -0.0123      0.231     -0.053      0.957      -0.464       0.440
x271           0.0025      0.003      0.801      0.423      -0.004       0.009
x272           0.0130      0.009      1.414      0.157      -0.005       0.031
x273           0.0108      0.002      4.330      0.000       0.006       0.016
x274          -0.0026      0.002     -1.618      0.106      -0.006       0.001
x275          -0.0041      0.002     -1.722      0.085      -0.009       0.001
x276          -0.0016      0.002     -0.730      0.466      -0.006       0.003
x277          -0.0251      0.188     -0.133      0.894      -0.394       0.344
x278          -0.2523      0.139     -1.821      0.069      -0.524       0.019
x279          -0.0027      0.001     -3.276      0.001      -0.004      -0.001
x280           0.0263      0.053      0.500      0.617      -0.077       0.129
x281          -0.0518      0.033     -1.567      0.117      -0.117       0.013
x282           0.0455      0.050      0.910      0.363      -0.052       0.143
x283          -0.0618      0.087     -0.711      0.477      -0.232       0.109
x284          -0.0006      0.000     -1.654      0.098      -0.001       0.000
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x286           0.0096      0.005      1.884      0.060      -0.000       0.020
x287          -0.0090      0.006     -1.489      0.136      -0.021       0.003
x288       -4.208e-05      0.001     -0.035      0.972      -0.002       0.002
x289        1.255e-06   2.44e-05      0.051      0.959   -4.67e-05    4.92e-05
x290          -0.4771      0.234     -2.039      0.042      -0.936      -0.018
x291       -1.363e-05    8.5e-06     -1.604      0.109   -3.03e-05    3.03e-06
x292        2.347e-06   2.88e-05      0.082      0.935    -5.4e-05    5.87e-05
x293          -0.0051      0.002     -2.113      0.035      -0.010      -0.000
x294           0.0031      0.004      0.722      0.470      -0.005       0.011
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x296           0.1255      0.179      0.701      0.483      -0.225       0.476
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x298           0.0009      0.001      1.047      0.295      -0.001       0.003
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x300           0.0067      0.008      0.835      0.404      -0.009       0.023
x301           0.3602      0.201      1.795      0.073      -0.033       0.754
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x312           0.0650      0.027      2.384      0.017       0.012       0.118
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x316           7.1643      2.521      2.842      0.004       2.223      12.105
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x321          -0.0016      0.004     -0.407      0.684      -0.009       0.006
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x324           5.0574      2.184      2.316      0.021       0.777       9.338
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x326         120.1390     81.914      1.467      0.143     -40.429     280.707
x327          67.7409    102.872      0.658      0.510    -133.909     269.391
x328           1.2264      0.405      3.026      0.002       0.432       2.021
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x330           3.4402      3.328      1.034      0.301      -3.083       9.964
x331          10.5558     86.254      0.122      0.903    -158.519     179.631
x332          -1.8243      1.155     -1.579      0.114      -4.089       0.440
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x334          -2.4291      0.965     -2.518      0.012      -4.320      -0.538
x335          -0.3880      0.629     -0.617      0.538      -1.621       0.845
x336           4.3435      0.999      4.346      0.000       2.384       6.303
x337          -0.6000      0.939     -0.639      0.523      -2.441       1.240
x338         -43.3300     69.411     -0.624      0.532    -179.390      92.730
x339         -64.4199     53.055     -1.214      0.225    -168.419      39.579
x340           0.4637      0.304      1.525      0.127      -0.132       1.060
x341          -8.8768     19.064     -0.466      0.641     -46.246      28.493
x342          30.8993     11.598      2.664      0.008       8.164      53.634
x343           6.6887     22.805      0.293      0.769     -38.014      51.392
x344         -41.3147     34.996     -1.181      0.238    -109.914      27.284
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x347           0.0032      0.010      0.313      0.754      -0.017       0.023
x348           0.0003      0.000      0.995      0.320      -0.000       0.001
x349           1.9549      2.364      0.827      0.408      -2.679       6.589
x350        2.859e-05   9.37e-05      0.305      0.760      -0.000       0.000
x351          -0.0004      0.000     -1.478      0.139      -0.001       0.000
x352           0.0795      0.022      3.543      0.000       0.036       0.123
x353          -0.1445      0.041     -3.508      0.000      -0.225      -0.064
x354           0.0840      0.030      2.811      0.005       0.025       0.143
x355           1.2028      2.004      0.600      0.548      -2.725       5.131
x356          -4.0621      2.320     -1.751      0.080      -8.610       0.486
x357           0.0124      0.009      1.316      0.188      -0.006       0.031
x358           0.0400      0.021      1.866      0.062      -0.002       0.082
x359           0.0214      0.073      0.293      0.769      -0.122       0.164
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x361           0.0021      0.028      0.077      0.939      -0.052       0.056
x362           0.0874      0.081      1.079      0.281      -0.071       0.246
x363           0.0139      0.021      0.670      0.503      -0.027       0.055
x364           0.0216      0.014      1.588      0.112      -0.005       0.048
x365           0.0171      0.025      0.688      0.492      -0.032       0.066
x366          -0.0811      0.021     -3.826      0.000      -0.123      -0.040
x367           0.7498      1.552      0.483      0.629      -2.293       3.793
x368          -0.0492      1.175     -0.042      0.967      -2.353       2.254
x369          -0.0028      0.006     -0.429      0.668      -0.015       0.010
x370          -1.7811      0.436     -4.087      0.000      -2.635      -0.927
x371          -0.4033      0.286     -1.409      0.159      -0.964       0.158
x372          -0.1746      0.357     -0.488      0.625      -0.875       0.526
x373          -1.0035      0.745     -1.347      0.178      -2.464       0.457
x374          -0.1188      0.047     -2.510      0.012      -0.212      -0.026
x375          -0.0067      0.011     -0.591      0.555      -0.029       0.015
x376          -0.0004      0.000     -1.406      0.160      -0.001       0.000
x377          -2.5849      2.835     -0.912      0.362      -8.141       2.971
x378        7.469e-06      0.000      0.070      0.944      -0.000       0.000
x379           0.0005      0.000      1.540      0.123      -0.000       0.001
x380          -0.0884      0.026     -3.410      0.001      -0.139      -0.038
x381           0.1489      0.049      3.031      0.002       0.053       0.245
x382          -0.0989      0.036     -2.773      0.006      -0.169      -0.029
x383           0.4968      2.250      0.221      0.825      -3.914       4.908
x384           4.6910      2.565      1.829      0.067      -0.338       9.720
x385          -0.0066      0.011     -0.602      0.547      -0.028       0.015
x386          -0.0368      0.025     -1.491      0.136      -0.085       0.012
x387          -0.0084      0.076     -0.110      0.912      -0.158       0.141
x388           1.3827      2.131      0.649      0.516      -2.794       5.559
x389          -0.0058      0.031     -0.186      0.853      -0.067       0.056
x390          -0.0931      0.090     -1.039      0.299      -0.269       0.082
x391           0.0090      0.025      0.365      0.715      -0.039       0.057
x392          -0.0338      0.017     -2.044      0.041      -0.066      -0.001
x393          -0.0264      0.029     -0.914      0.360      -0.083       0.030
x394           0.0893      0.025      3.575      0.000       0.040       0.138
x395          -0.8046      1.850     -0.435      0.664      -4.430       2.821
x396          -0.5845      1.412     -0.414      0.679      -3.351       2.182
x397          -0.0038      0.008     -0.497      0.619      -0.019       0.011
x398           1.8264      0.483      3.778      0.000       0.879       2.774
x399           0.4237      0.345      1.226      0.220      -0.254       1.101
x400           0.4106      0.415      0.988      0.323      -0.404       1.225
x401           0.1998      0.899      0.222      0.824      -1.562       1.962
x402           0.0024      0.001      1.676      0.094      -0.000       0.005
x403        8.296e-05   4.68e-05      1.772      0.076   -8.81e-06       0.000
x404          -0.0483      0.507     -0.095      0.924      -1.042       0.945
x405        3.349e-05   1.73e-05      1.932      0.053   -4.96e-07    6.75e-05
x406       -8.709e-05   4.88e-05     -1.785      0.074      -0.000    8.55e-06
x407          -0.0014      0.005     -0.309      0.757      -0.010       0.007
x408           0.0053      0.008      0.673      0.501      -0.010       0.021
x409          -0.0004      0.006     -0.069      0.945      -0.012       0.011
x410          -0.8054      0.384     -2.096      0.036      -1.559      -0.052
x411           1.0059      0.455      2.210      0.027       0.114       1.898
x412          -0.0008      0.002     -0.431      0.667      -0.004       0.003
x413           0.0045      0.004      0.994      0.320      -0.004       0.013
x414          -0.0021      0.011     -0.186      0.852      -0.024       0.020
x415           0.0140      0.377      0.037      0.970      -0.725       0.753
x416          -0.0106      0.005     -2.172      0.030      -0.020      -0.001
x417           0.0003      0.013      0.023      0.982      -0.026       0.026
x418          -0.0208      0.004     -4.705      0.000      -0.029      -0.012
x419          -0.0007      0.003     -0.215      0.830      -0.007       0.005
x420           0.0147      0.005      3.177      0.001       0.006       0.024
x421           0.0035      0.004      0.813      0.416      -0.005       0.012
x422           0.2089      0.344      0.607      0.544      -0.466       0.884
x423          -0.2785      0.278     -1.003      0.316      -0.823       0.266
x424           0.0053      0.001      3.915      0.000       0.003       0.008
x425           0.0439      0.075      0.582      0.561      -0.104       0.192
x426          -0.0477      0.067     -0.706      0.480      -0.180       0.085
x427          -0.2251      0.077     -2.940      0.003      -0.375      -0.075
x428           0.4803      0.164      2.923      0.003       0.158       0.802
x429       -2.317e-06   7.55e-07     -3.071      0.002    -3.8e-06   -8.38e-07
x430           0.0362      0.012      2.995      0.003       0.013       0.060
x431         5.73e-07   4.16e-07      1.376      0.169   -2.43e-07    1.39e-06
x432        6.378e-07   1.07e-06      0.598      0.550   -1.45e-06    2.73e-06
x433          -0.0002   9.62e-05     -1.704      0.088      -0.000    2.46e-05
x434       -3.293e-05      0.000     -0.167      0.868      -0.000       0.000
x435           0.0001      0.000      0.990      0.322      -0.000       0.000
x436          -0.0117      0.009     -1.352      0.177      -0.029       0.005
x437          -0.0008      0.010     -0.083      0.934      -0.021       0.019
x438        3.306e-05   4.05e-05      0.817      0.414   -4.63e-05       0.000
x439       -4.888e-05   9.28e-05     -0.527      0.598      -0.000       0.000
x440           0.0006      0.000      2.142      0.032    5.14e-05       0.001
x441          -0.0061      0.009     -0.687      0.492      -0.024       0.011
x442         7.02e-05      0.000      0.621      0.535      -0.000       0.000
x443        6.417e-05      0.000      0.201      0.840      -0.001       0.001
x444           0.0002      0.000      1.824      0.068   -1.55e-05       0.000
x445        -1.12e-05   7.31e-05     -0.153      0.878      -0.000       0.000
x446        -1.58e-05      0.000     -0.134      0.893      -0.000       0.000
x447       -1.618e-05   9.71e-05     -0.167      0.868      -0.000       0.000
x448           0.0018      0.008      0.223      0.823      -0.014       0.018
x449          -0.0167      0.006     -2.762      0.006      -0.029      -0.005
x450       -7.894e-05   3.61e-05     -2.188      0.029      -0.000   -8.22e-06
x451          -0.0008      0.002     -0.443      0.658      -0.004       0.003
x452          -0.0001      0.001     -0.083      0.933      -0.003       0.003
x453          -0.0008      0.002     -0.504      0.614      -0.004       0.002
x454          -0.0015      0.004     -0.382      0.702      -0.009       0.006
x455          84.5025     69.775      1.211      0.226     -52.270     221.275
x456          -0.0043      0.005     -0.960      0.337      -0.013       0.005
x457           0.0475      0.013      3.528      0.000       0.021       0.074
x458           2.2225      0.939      2.367      0.018       0.382       4.063
x459           0.4095      1.906      0.215      0.830      -3.326       4.145
x460          -0.7919      1.381     -0.573      0.567      -3.500       1.916
x461         102.3906     86.156      1.188      0.235     -66.491     271.272
x462        -129.3163    107.180     -1.207      0.228    -339.410      80.778
x463          -0.1336      0.377     -0.354      0.723      -0.873       0.606
x464           0.3182      1.064      0.299      0.765      -1.767       2.403
x465         -10.5371      3.509     -3.003      0.003     -17.416      -3.658
x466         -42.0328     90.031     -0.467      0.641    -218.512     134.446
x467           3.8891      1.109      3.508      0.000       1.716       6.062
x468          -9.4498      3.931     -2.404      0.016     -17.155      -1.745
x469          -3.1036      0.864     -3.594      0.000      -4.796      -1.411
x470           0.8854      0.608      1.457      0.145      -0.306       2.076
x471           2.7692      1.061      2.611      0.009       0.690       4.848
x472          -1.6663      0.955     -1.744      0.081      -3.539       0.207
x473          55.8013     71.365      0.782      0.434     -84.088     195.691
x474         196.0232     52.945      3.702      0.000      92.241     299.805
x475           0.6501      0.299      2.174      0.030       0.064       1.236
x476          11.0061     21.090      0.522      0.602     -30.335      52.347
x477          -5.6901     12.040     -0.473      0.637     -29.292      17.912
x478         -38.9068     19.247     -2.021      0.043     -76.635      -1.179
x479           1.6630     36.472      0.046      0.964     -69.828      73.154
x480        1.365e-07   9.48e-08      1.440      0.150   -4.94e-08    3.22e-07
x481        2.066e-07   3.64e-07      0.567      0.571   -5.08e-07    9.21e-07
x482       -3.507e-06   3.45e-05     -0.102      0.919   -7.11e-05    6.41e-05
x483        1.593e-05   6.38e-05      0.250      0.803      -0.000       0.000
x484       -1.091e-05   4.82e-05     -0.226      0.821      -0.000    8.36e-05
x485           0.0034      0.003      1.108      0.268      -0.003       0.010
x486          -0.0042      0.004     -1.168      0.243      -0.011       0.003
x487       -9.337e-06    1.4e-05     -0.665      0.506   -3.68e-05    1.82e-05
x488        4.381e-05   3.87e-05      1.132      0.258   -3.21e-05       0.000
x489        9.368e-05      0.000      0.885      0.376      -0.000       0.000
x490          -0.0052      0.003     -1.586      0.113      -0.012       0.001
x491       -6.163e-05   4.37e-05     -1.411      0.158      -0.000     2.4e-05
x492          -0.0003      0.000     -2.797      0.005      -0.001   -9.67e-05
x493        -4.65e-05   3.47e-05     -1.339      0.181      -0.000    2.16e-05
x494        4.474e-05   2.34e-05      1.908      0.056   -1.22e-06    9.07e-05
x495        3.771e-05   3.55e-05      1.062      0.288   -3.19e-05       0.000
x496       -4.653e-05   3.19e-05     -1.458      0.145      -0.000     1.6e-05
x497          -0.0046      0.003     -1.693      0.091      -0.010       0.001
x498           0.0049      0.002      2.381      0.017       0.001       0.009
x499        4.363e-06   1.12e-05      0.388      0.698   -1.77e-05    2.64e-05
x500          -0.0011      0.001     -1.643      0.101      -0.002       0.000
x501          -0.0004      0.000     -0.799      0.424      -0.001       0.001
x502          -0.0011      0.001     -1.882      0.060      -0.002    4.59e-05
x503          -0.0007      0.001     -0.546      0.585      -0.003       0.002
x504        6.374e-07   7.31e-07      0.871      0.384   -7.96e-07    2.07e-06
x505           0.0003   9.89e-05      2.960      0.003    9.89e-05       0.000
x506          -0.0005      0.000     -2.382      0.017      -0.001   -8.49e-05
x507           0.0002      0.000      1.304      0.192      -0.000       0.001
x508          -0.0005      0.009     -0.060      0.953      -0.018       0.017
x509           0.0079      0.011      0.745      0.456      -0.013       0.029
x510        3.199e-05   3.84e-05      0.832      0.405   -4.33e-05       0.000
x511        6.857e-05   8.47e-05      0.810      0.418   -9.74e-05       0.000
x512          -0.0004      0.000     -1.690      0.091      -0.001    6.94e-05
x513          -0.0170      0.010     -1.774      0.076      -0.036       0.002
x514           0.0002      0.000      2.278      0.023     3.3e-05       0.000
x515          -0.0007      0.000     -2.374      0.018      -0.001      -0.000
x516           0.0002      0.000      1.705      0.088   -2.75e-05       0.000
x517          -0.0002   8.08e-05     -2.170      0.030      -0.000   -1.69e-05
x518          -0.0004      0.000     -3.089      0.002      -0.001      -0.000
x519           0.0003      0.000      2.498      0.012    6.01e-05       0.000
x520           0.0061      0.008      0.761      0.446      -0.010       0.022
x521           0.0141      0.007      1.980      0.048       0.000       0.028
x522        2.858e-06   3.27e-05      0.087      0.930   -6.13e-05     6.7e-05
x523           0.0007      0.002      0.438      0.661      -0.003       0.004
x524          -0.0031      0.002     -1.921      0.055      -0.006    6.24e-05
x525           0.0012      0.002      0.761      0.446      -0.002       0.004
x526           0.0090      0.004      2.259      0.024       0.001       0.017
x527          -0.0260      0.006     -4.021      0.000      -0.039      -0.013
x528           0.0555      0.021      2.699      0.007       0.015       0.096
x529          -0.0312      0.014     -2.244      0.025      -0.058      -0.004
x530           0.4053      0.897      0.452      0.652      -1.354       2.164
x531           3.8216      0.986      3.878      0.000       1.890       5.753
x532           0.0052      0.003      1.506      0.132      -0.002       0.012
x533           0.0086      0.010      0.838      0.402      -0.012       0.029
x534           0.0480      0.025      1.905      0.057      -0.001       0.097
x535          -0.4076      0.701     -0.581      0.561      -1.783       0.968
x536          -0.0281      0.009     -3.022      0.003      -0.046      -0.010
x537          -0.0330      0.028     -1.161      0.246      -0.089       0.023
x538          -0.0066      0.009     -0.723      0.469      -0.025       0.011
x539           0.0177      0.006      3.138      0.002       0.007       0.029
x540           0.0011      0.008      0.131      0.896      -0.015       0.018
x541          -0.0074      0.007     -1.004      0.315      -0.022       0.007
x542          -0.6955      0.687     -1.012      0.312      -2.043       0.652
x543           1.0805      0.474      2.278      0.023       0.151       2.010
x544           0.0002      0.003      0.079      0.937      -0.005       0.006
x545           0.1599      0.156      1.028      0.304      -0.145       0.465
x546          -0.0657      0.109     -0.602      0.547      -0.280       0.148
x547          -0.1182      0.163     -0.727      0.467      -0.437       0.201
x548           0.4114      0.299      1.378      0.168      -0.174       0.997
x549          -0.0185      0.022     -0.832      0.406      -0.062       0.025
x550           0.0209      0.028      0.739      0.460      -0.035       0.076
x551           0.6030      1.556      0.388      0.698      -2.446       3.652
x552          -4.8318      1.720     -2.809      0.005      -8.204      -1.460
x553          -0.0182      0.007     -2.588      0.010      -0.032      -0.004
x554           0.0105      0.022      0.471      0.638      -0.033       0.054
x555          -0.0866      0.052     -1.661      0.097      -0.189       0.016
x556           1.3961      1.431      0.976      0.329      -1.408       4.200
x557           0.0512      0.020      2.611      0.009       0.013       0.090
x558           0.0925      0.060      1.540      0.124      -0.025       0.210
x559           0.0370      0.016      2.342      0.019       0.006       0.068
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x561          -0.0086      0.015     -0.561      0.575      -0.039       0.021
x562           0.0029      0.016      0.187      0.851      -0.028       0.033
x563          -0.3128      1.271     -0.246      0.806      -2.804       2.178
x564          -1.1920      0.899     -1.325      0.185      -2.955       0.571
x565          -0.0082      0.005     -1.596      0.111      -0.018       0.002
x566           0.1194      0.298      0.401      0.689      -0.465       0.704
x567           0.0878      0.202      0.434      0.664      -0.309       0.484
x568          -0.2011      0.301     -0.667      0.505      -0.792       0.390
x569          -1.5445      0.568     -2.721      0.007      -2.657      -0.432
x570          -0.0080      0.011     -0.712      0.477      -0.030       0.014
x571          -0.3898      1.110     -0.351      0.725      -2.565       1.786
x572           2.6146      1.343      1.946      0.052      -0.019       5.248
x573           0.0158      0.005      2.892      0.004       0.005       0.027
x574          -0.0163      0.015     -1.070      0.284      -0.046       0.014
x575           0.0785      0.040      1.947      0.052      -0.001       0.157
x576          -1.3285      1.050     -1.266      0.206      -3.386       0.729
x577          -0.0354      0.015     -2.434      0.015      -0.064      -0.007
x578          -0.0774      0.046     -1.693      0.090      -0.167       0.012
x579          -0.0098      0.010     -0.941      0.347      -0.030       0.011
x580           0.0142      0.006      2.353      0.019       0.002       0.026
x581          -0.0119      0.011     -1.102      0.271      -0.033       0.009
x582           0.0129      0.011      1.160      0.246      -0.009       0.035
x583           0.4968      0.928      0.536      0.592      -1.322       2.315
x584           0.1200      0.603      0.199      0.842      -1.062       1.302
x585           0.0039      0.004      1.020      0.308      -0.004       0.011
x586          -0.1353      0.229     -0.591      0.555      -0.584       0.314
x587          -0.0705      0.134     -0.528      0.598      -0.332       0.191
x588           0.1929      0.212      0.909      0.364      -0.223       0.609
x589           0.9730      0.406      2.394      0.017       0.176       1.770
x590          18.1319     49.528      0.366      0.714     -78.952     115.216
x591        -142.4630     78.516     -1.814      0.070    -296.369      11.443
x592           0.1151      0.375      0.307      0.759      -0.620       0.850
x593          -0.8042      1.024     -0.786      0.432      -2.811       1.202
x594          -0.9045      2.597     -0.348      0.728      -5.996       4.187
x595          -9.7365     66.754     -0.146      0.884    -140.588     121.115
x596           1.4307      0.918      1.558      0.119      -0.370       3.231
x597           1.7337      2.476      0.700      0.484      -3.120       6.588
x598           0.4414      0.752      0.587      0.557      -1.032       1.914
x599          -1.4706      0.488     -3.014      0.003      -2.427      -0.514
x600           1.2537      0.751      1.668      0.095      -0.219       2.727
x601           0.6768      0.662      1.022      0.307      -0.621       1.975
x602          40.3777     58.320      0.692      0.489     -73.941     154.697
x603        -138.8041     38.376     -3.617      0.000    -214.030     -63.579
x604          -0.3156      0.256     -1.234      0.217      -0.817       0.186
x605           4.3339     15.765      0.275      0.783     -26.569      35.237
x606         -16.4019     10.129     -1.619      0.105     -36.256       3.452
x607         -20.6523     14.395     -1.435      0.151     -48.870       7.565
x608         -28.1073     28.876     -0.973      0.330     -84.710      28.495
x609         -72.3131     56.827     -1.273      0.203    -183.706      39.080
x610          -0.8800      0.450     -1.955      0.051      -1.762       0.002
x611           1.2025      1.236      0.973      0.331      -1.221       3.626
x612         -10.0382      2.927     -3.430      0.001     -15.775      -4.302
x613         147.1581     79.380      1.854      0.064      -8.443     302.759
x614           2.4391      1.106      2.206      0.027       0.271       4.607
x615           7.4115      2.894      2.561      0.010       1.738      13.085
x616          -0.6717      0.870     -0.772      0.440      -2.377       1.034
x617          -0.9819      0.586     -1.676      0.094      -2.130       0.166
x618           0.2841      0.827      0.343      0.731      -1.338       1.906
x619           0.5577      0.701      0.795      0.427      -0.817       1.933
x620         -51.0351     65.869     -0.775      0.438    -180.151      78.081
x621          81.8123     47.591      1.719      0.086     -11.476     175.101
x622           0.1679      0.269      0.624      0.533      -0.360       0.696
x623          22.1976     17.533      1.266      0.206     -12.170      56.565
x624         -10.3082     11.595     -0.889      0.374     -33.036      12.420
x625           0.3580     16.933      0.021      0.983     -32.835      33.551
x626          56.3773     33.664      1.675      0.094      -9.610     122.365
x627           0.0016      0.001      1.619      0.105      -0.000       0.004
x628          -0.0035      0.004     -0.960      0.337      -0.011       0.004
x629           0.0146      0.010      1.468      0.142      -0.005       0.034
x630          -0.0065      0.287     -0.023      0.982      -0.570       0.557
x631          -0.0069      0.004     -1.894      0.058      -0.014       0.000
x632          -0.0084      0.011     -0.753      0.451      -0.030       0.013
x633           0.0019      0.003      0.548      0.584      -0.005       0.009
x634          -0.0008      0.002     -0.346      0.729      -0.005       0.004
x635           0.0031      0.003      0.913      0.361      -0.004       0.010
x636          -0.0001      0.003     -0.046      0.964      -0.006       0.006
x637          -0.0588      0.272     -0.217      0.829      -0.591       0.474
x638          -0.6415      0.194     -3.300      0.001      -1.023      -0.260
x639          -0.0019      0.001     -1.588      0.112      -0.004       0.000
x640          -0.0626      0.068     -0.926      0.354      -0.195       0.070
x641           0.0218      0.045      0.484      0.628      -0.067       0.110
x642           0.0136      0.063      0.215      0.830      -0.110       0.137
x643          -0.0161      0.123     -0.130      0.896      -0.258       0.226
x644          -0.0017      0.006     -0.301      0.763      -0.013       0.009
x645          -0.0319      0.020     -1.610      0.107      -0.071       0.007
x646          -0.8730      0.819     -1.066      0.286      -2.478       0.732
x647          -0.0064      0.010     -0.664      0.507      -0.025       0.012
x648           0.0057      0.024      0.239      0.811      -0.041       0.052
x649          -0.0243      0.010     -2.413      0.016      -0.044      -0.005
x650           0.0204      0.007      3.031      0.002       0.007       0.034
x651           0.0076      0.010      0.762      0.446      -0.012       0.027
x652          -0.0014      0.009     -0.153      0.879      -0.019       0.016
x653           0.1457      0.679      0.215      0.830      -1.186       1.477
x654           1.6526      0.535      3.087      0.002       0.603       2.702
x655           0.0041      0.003      1.369      0.171      -0.002       0.010
x656          -0.0205      0.158     -0.130      0.897      -0.330       0.289
x657          -0.1734      0.156     -1.115      0.265      -0.478       0.131
x658           0.0678      0.144      0.470      0.638      -0.215       0.351
x659           0.8389      0.373      2.249      0.025       0.108       1.570
x660          -0.0376      0.044     -0.863      0.388      -0.123       0.048
x661           3.8362      2.637      1.455      0.146      -1.333       9.006
x662          -0.0385      0.031     -1.258      0.208      -0.099       0.021
x663           0.0675      0.072      0.933      0.351      -0.074       0.209
x664          -0.1041      0.033     -3.136      0.002      -0.169      -0.039
x665          -0.0037      0.026     -0.143      0.886      -0.054       0.047
x666           0.0954      0.034      2.789      0.005       0.028       0.162
x667          -0.0273      0.029     -0.956      0.339      -0.083       0.029
x668           2.9491      2.334      1.264      0.206      -1.626       7.524
x669          -0.3324      1.784     -0.186      0.852      -3.829       3.164
x670           0.0367      0.009      3.968      0.000       0.019       0.055
x671          -0.3301      0.531     -0.621      0.534      -1.371       0.711
x672          -0.7283      0.452     -1.610      0.107      -1.615       0.158
x673          -0.4449      0.389     -1.145      0.252      -1.207       0.317
x674           0.7306      1.135      0.644      0.520      -1.493       2.955
x675          23.6104     46.134      0.512      0.609     -66.820     114.041
x676          -1.6146      0.898     -1.799      0.072      -3.374       0.145
x677           2.4907      3.035      0.821      0.412      -3.458       8.440
x678           1.1637      0.708      1.645      0.100      -0.223       2.551
x679           1.6533      0.465      3.555      0.000       0.742       2.565
x680          -2.3067      0.753     -3.065      0.002      -3.782      -0.831
x681           0.3580      0.700      0.511      0.609      -1.014       1.730
x682        -104.7675     56.358     -1.859      0.063    -215.241       5.706
x683          81.3876     40.264      2.021      0.043       2.463     160.312
x684          -0.4671      0.233     -2.009      0.045      -0.923      -0.011
x685           9.0917     14.572      0.624      0.533     -19.472      37.655
x686          49.6670      9.955      4.989      0.000      30.152      69.182
x687          27.9889     13.784      2.030      0.042       0.969      55.009
x688         -87.2089     27.718     -3.146      0.002    -141.542     -32.876
x689           0.0036      0.008      0.476      0.634      -0.011       0.018
x690           0.0249      0.030      0.834      0.404      -0.034       0.084
x691           0.0255      0.011      2.386      0.017       0.005       0.046
x692          -0.0005      0.007     -0.073      0.942      -0.014       0.013
x693          -0.0148      0.010     -1.436      0.151      -0.035       0.005
x694           0.0013      0.009      0.143      0.886      -0.016       0.019
x695          -2.1685      0.816     -2.657      0.008      -3.768      -0.569
x696           0.7453      0.536      1.389      0.165      -0.306       1.797
x697          -0.0116      0.004     -3.324      0.001      -0.019      -0.005
x698           0.0425      0.183      0.232      0.817      -0.316       0.401
x699           0.1119      0.116      0.962      0.336      -0.116       0.340
x700           0.1748      0.171      1.020      0.308      -0.161       0.511
x701          -0.5357      0.336     -1.596      0.111      -1.194       0.122
x702          -0.0116      0.048     -0.243      0.808      -0.105       0.082
x703           0.0471      0.035      1.347      0.178      -0.021       0.116
x704           0.0469      0.029      1.591      0.112      -0.011       0.105
x705          -0.0797      0.035     -2.260      0.024      -0.149      -0.011
x706           0.0018      0.033      0.054      0.957      -0.062       0.066
x707          -4.1870      2.313     -1.810      0.070      -8.721       0.347
x708           5.3006      2.053      2.582      0.010       1.277       9.325
x709          -0.0210      0.009     -2.236      0.025      -0.039      -0.003
x710           0.2767      0.537      0.515      0.606      -0.776       1.329
x711           1.9576      0.470      4.164      0.000       1.036       2.879
x712           1.1577      0.456      2.540      0.011       0.264       2.051
x713          -2.9963      1.201     -2.496      0.013      -5.350      -0.643
x714          -0.0005      0.004     -0.125      0.901      -0.009       0.008
x715          -0.0299      0.005     -6.037      0.000      -0.040      -0.020
x716          -0.0106      0.009     -1.227      0.220      -0.027       0.006
x717           0.0254      0.007      3.468      0.001       0.011       0.040
x718           2.0175      0.654      3.086      0.002       0.736       3.299
x719          -0.3858      0.403     -0.958      0.338      -1.175       0.404
x720           0.0091      0.003      3.232      0.001       0.004       0.015
x721          -0.1431      0.156     -0.917      0.359      -0.449       0.163
x722           0.2884      0.099      2.899      0.004       0.093       0.483
x723          -0.1046      0.172     -0.607      0.544      -0.442       0.233
x724          -1.0920      0.294     -3.711      0.000      -1.669      -0.515
x725           0.0083      0.002      4.020      0.000       0.004       0.012
x726           0.0215      0.006      3.650      0.000       0.010       0.033
x727          -0.0197      0.006     -3.177      0.001      -0.032      -0.008
x728           0.1610      0.380      0.424      0.672      -0.584       0.906
x729           0.2289      0.291      0.787      0.431      -0.341       0.799
x730           0.0036      0.002      2.128      0.033       0.000       0.007
x731          -0.1016      0.113     -0.899      0.369      -0.323       0.120
x732           0.0033      0.058      0.057      0.954      -0.110       0.117
x733          -0.1484      0.116     -1.282      0.200      -0.375       0.078
x734           0.3794      0.166      2.292      0.022       0.055       0.704
x735           0.0121      0.006      1.908      0.056      -0.000       0.025
x736          -0.0193      0.008     -2.440      0.015      -0.035      -0.004
x737          -2.5094      0.801     -3.134      0.002      -4.079      -0.940
x738           0.6283      0.465      1.353      0.176      -0.282       1.539
x739          -0.0067      0.003     -2.498      0.013      -0.012      -0.001
x740          -0.2402      0.173     -1.388      0.165      -0.579       0.099
x741          -0.1823      0.106     -1.726      0.084      -0.389       0.025
x742           0.7772      0.190      4.084      0.000       0.404       1.150
x743           0.1244      0.316      0.393      0.694      -0.496       0.745
x744           0.0101      0.005      2.095      0.036       0.001       0.019
x745           1.0569      0.629      1.680      0.093      -0.177       2.290
x746          -1.0767      0.478     -2.254      0.024      -2.013      -0.140
x747          -0.0002      0.003     -0.080      0.937      -0.005       0.005
x748           0.1649      0.157      1.051      0.293      -0.143       0.472
x749          -0.0625      0.093     -0.675      0.500      -0.244       0.119
x750          -0.4843      0.175     -2.776      0.006      -0.826      -0.142
x751           0.1818      0.266      0.684      0.494      -0.339       0.703
x752          12.1158     37.689      0.321      0.748     -61.761      85.993
x753           2.5148     36.081      0.070      0.944     -68.212      73.241
x754          -0.4163      0.243     -1.712      0.087      -0.893       0.060
x755          46.0265     12.858      3.580      0.000      20.822      71.231
x756          -7.6812      8.305     -0.925      0.355     -23.960       8.597
x757         -11.6182     11.607     -1.001      0.317     -34.369      11.133
x758          37.7241     22.325      1.690      0.091      -6.037      81.486
x759          -3.0465     18.142     -0.168      0.867     -38.608      32.515
x760           0.0694      0.137      0.506      0.613      -0.199       0.338
x761         -15.6018      9.265     -1.684      0.092     -33.764       2.560
x762         -21.8181      5.236     -4.167      0.000     -32.081     -11.555
x763         -26.5955      9.972     -2.667      0.008     -46.142      -7.049
x764          95.6318     15.702      6.090      0.000      64.852     126.411
x765          -0.0014      0.001     -2.512      0.012      -0.002      -0.000
x766           0.1493      0.052      2.853      0.004       0.047       0.252
x767          -0.0976      0.035     -2.758      0.006      -0.167      -0.028
x768           0.0161      0.051      0.314      0.754      -0.084       0.117
x769           0.3641      0.100      3.626      0.000       0.167       0.561
x770           0.5061      2.065      0.245      0.806      -3.542       4.554
x771          -2.8247      2.585     -1.093      0.275      -7.892       2.243
x772          -0.6597      2.676     -0.247      0.805      -5.905       4.586
x773          15.9488      6.562      2.431      0.015       3.087      28.811
x774           1.3191      0.901      1.464      0.143      -0.447       3.085
x775           0.9776      2.501      0.391      0.696      -3.924       5.879
x776          -7.3609      4.636     -1.588      0.112     -16.448       1.726
x777           1.1157      1.893      0.589      0.556      -2.595       4.826
x778         -12.9081      6.263     -2.061      0.039     -25.184      -0.632
x779          32.6915      7.728      4.230      0.000      17.543      47.840
==============================================================================
Omnibus:                     1429.179   Durbin-Watson:                   2.005
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             3371.878
Skew:                          -0.763   Prob(JB):                         0.00
Kurtosis:                       5.247   Cond. No.                     3.16e+11
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.16e+11. This might indicate that there are
strong multicollinearity or other numerical problems.

Al ser un modelo polinomial de segundo grado basado en 38 variables, es difícil interpretar a la perfección cada uno de los coeficientes, ya que son un total de 779. Sin embargo se pueden realizar algunas inferencias.

Por ejemplo:

  • El término x^5 reduce la temperatura crítica de un superconductor entre -4.417 y -0.85 grados con un 95% de confianza.
  • El término x^117 aumenta la temperatura crítica de un superconductor entre 0.038 y 0.103 grados con un 95% de confianza.
  • El término x^424 aumenta la tempratura crítica de un superconductor entre 0.003 y 0.008 grados con un 95% de confianza.

En general, utilizando estos datos y el modelo, se pueden obtener conclusiones del efecto de las variables en la temperatura crítica. Aún así, no se puede saber el efecto específico de cada variable, ya que al tener varias y trabajar con una regresión polinomial de grado 2, cada término representa no solo el cuadrado de cada variable si no también las interacciones entre cada par de variables posibles.

Con esto en mente, se puede concluir que el modelo es bueno para realizar predicciones, sin embargo, para realizar inferencias, sería mejor considerar modelos más interpretables como la regresión lineal.

Referencias:

  • UCI Machine Learning Repository
  • A Data-Driven Statistical Model for Predicting the Critical Temperature of a Superconductor